Nonparametric learning for complex data: applications in environmental data modeling, surface-based data analysis, and neuroimaging studies
Date
2024-08
Authors
Gu, Zhiling
Major Professor
Advisor
Wang, Lily
Nettleton, Dan
Chu, Lynna
Liu, Peng
Maitra, Ranjan
Committee Member
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Abstract
The first project proposes a novel nonparametric method, Triangulated Spherical Spline Smoothing (TSSS), for surface-based data analysis. TSSS employs penalized splines on a triangulation of surface patches, effectively addressing boundary effects and enhancing computational efficiency. Theoretical guarantees, including optimal convergence rates and asymptotic normality, are established. Applications to cortical surface functional magnetic resonance imaging (fMRI) data and oceanic near-surface atmospheric data showcase TSSS's advantages in analyzing sparse and irregularly distributed data on complex domains.
The second project presents an advanced framework for statistical learning and inference of surface-based functional data, focusing on neuroimaging analysis. Integrating TSSS and next-generation function data analysis, the framework addresses challenges posed by complex surface-based domains and spatial dependencies. A novel approach for constructing simultaneous confidence corridors (SCCs) is introduced to quantify estimation uncertainty. The framework accommodates group comparisons, enabling the analysis of group differences or treatment effects. Numerical experiments and real-data analysis using cs-fMRI data from the Human Connectome Project Consortium (HCP) validate the proposed methods.
The third project introduces the Spatio-Temporally Varying Coefficient Models with Structure Identification (STVCoM-SI) framework to enhance the detection and interpretation of spatiotemporal heterogeneity in factors influencing response variables. By distinguishing between spatiotemporally varying and constant effects, STVCoM-SI improves computational efficiency and statistical power. Extensive simulations and an application to particulate matter (PM) data demonstrate the framework's ability to identify model structures accurately and improve prediction accuracy.
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Type
dissertation